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6-12 二叉搜索树的操作集（30分）
2022-08-10 17:54:00 【jie3606】
本题要求实现给定二叉搜索树的5种常用操作。
函数接口定义：
BinTree Insert( BinTree BST, ElementType X );
BinTree Delete( BinTree BST, ElementType X );
Position Find( BinTree BST, ElementType X );
Position FindMin( BinTree BST );
Position FindMax( BinTree BST );
其中BinTree结构定义如下：
typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
ElementType Data;
BinTree Left;
BinTree Right;
};
函数Insert将X插入二叉搜索树BST并返回结果树的根结点指针；
函数Delete将X从二叉搜索树BST中删除，并返回结果树的根结点指针；如果X不在树中，则打印一行Not Found并返回原树的根结点指针；
函数Find在二叉搜索树BST中找到X，返回该结点的指针；如果找不到则返回空指针；
函数 FindMin返回二叉搜索树BST中最小元结点的指针；
函数FindMax返回二叉搜索树BST中最大元结点的指针。
裁判测试程序样例：
#include <stdio.h>
#include <stdlib.h>
typedef int ElementType;
typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
ElementType Data;
BinTree Left;
BinTree Right;
};
void PreorderTraversal( BinTree BT ); /* 先序遍历，由裁判实现，细节不表 */
void InorderTraversal( BinTree BT ); /* 中序遍历，由裁判实现，细节不表 */
BinTree Insert( BinTree BST, ElementType X );
BinTree Delete( BinTree BST, ElementType X );
Position Find( BinTree BST, ElementType X );
Position FindMin( BinTree BST );
Position FindMax( BinTree BST );
int main()
{
BinTree BST, MinP, MaxP, Tmp;
ElementType X;
int N, i;
BST = NULL;
scanf("%d", &N);
for ( i=0; i<N; i++ ) {
scanf("%d", &X);
BST = Insert(BST, X);
}
printf("Preorder:"); PreorderTraversal(BST); printf("\n");
MinP = FindMin(BST);
MaxP = FindMax(BST);
scanf("%d", &N);
for( i=0; i<N; i++ ) {
scanf("%d", &X);
Tmp = Find(BST, X);
if (Tmp == NULL) printf("%d is not found\n", X);
else {
printf("%d is found\n", Tmp->Data);
if (Tmp==MinP) printf("%d is the smallest key\n", Tmp->Data);
if (Tmp==MaxP) printf("%d is the largest key\n", Tmp->Data);
}
}
scanf("%d", &N);
for( i=0; i<N; i++ ) {
scanf("%d", &X);
BST = Delete(BST, X);
}
printf("Inorder:"); InorderTraversal(BST); printf("\n");
return 0;
}
/* 你的代码将被嵌在这里 */
输入样例：
10
5 8 6 2 4 1 0 10 9 7
5
6 3 10 0 5
5
5 7 0 10 3
输出样例：
Preorder: 5 2 1 0 4 8 6 7 10 9
6 is found
3 is not found
10 is found
10 is the largest key
0 is found
0 is the smallest key
5 is found
Not Found
Inorder: 1 2 4 6 8 9
解答
BinTree Insert( BinTree BST, ElementType X ){
if(BST == NULL){
BinTree t = (BinTree) malloc(sizeof (BinTree));
t->Data = X;
t->Left = t->Right = NULL;
BST = t;
}
else
(X<BST->Data?(BST->Left = Insert(BST->Left,X)):(BST->Right=Insert(BST->Right,X)));
return BST;
}
BinTree Delete( BinTree BST, ElementType X ){
if(BST == NULL)
puts("Not Found");
else {
if (X == BST->Data) {
if (BST->Left != NULL && BST->Right != NULL) {
BinTree t = FindMax(BST->Left);
BST->Data = t->Data;
BST->Left = Delete(BST->Left, t->Data);
} else {
BST =(BST->Left ? BST->Left : BST->Right);
}
} else {
X > BST->Data ? (BST->Right = (Delete(BST->Right, X))) : (BST->Left = Delete(BST->Left, X));
}
}
return BST;
}
Position Find( BinTree BST, ElementType X ){
if(BST == NULL){
return NULL;
}
if(BST->Data == X){
return BST;
}
return X < BST->Data ? Find(BST->Left,X): Find(BST->Right,X);
}
Position FindMin( BinTree BST ){
if(BST != NULL) {
return BST->Left ? FindMin(BST->Left) : BST;
}
}
Position FindMax( BinTree BST ){
if(BST != NULL){
return BST->Right? FindMax(BST->Right):BST;
}
}
完整的代码
#include <stdio.h>
#include <stdlib.h>
typedef int ElementType;
typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
ElementType Data;
BinTree Left;
BinTree Right;
};
void PreorderTraversal( BinTree BT ); /* 先序遍历，由裁判实现，细节不表 */
void InorderTraversal( BinTree BT ); /* 中序遍历，由裁判实现，细节不表 */
BinTree Insert( BinTree BST, ElementType X );
BinTree Delete( BinTree BST, ElementType X );
Position Find( BinTree BST, ElementType X );
Position FindMin( BinTree BST );
Position FindMax( BinTree BST );
int main()
{
BinTree BST, MinP, MaxP, Tmp;
ElementType X;
int N, i;
BST = NULL;
scanf("%d", &N);
for ( i=0; i<N; i++ ) {
scanf("%d", &X);
BST = Insert(BST, X);
}
printf("Preorder:"); PreorderTraversal(BST); printf("\n");
MinP = FindMin(BST);
MaxP = FindMax(BST);
scanf("%d", &N);
for( i=0; i<N; i++ ) {
scanf("%d", &X);
Tmp = Find(BST, X);
if (Tmp == NULL) printf("%d is not found\n", X);
else {
printf("%d is found\n", Tmp->Data);
if (Tmp==MinP) printf("%d is the smallest key\n", Tmp->Data);
if (Tmp==MaxP) printf("%d is the largest key\n", Tmp->Data);
}
}
scanf("%d", &N);
for( i=0; i<N; i++ ) {
scanf("%d", &X);
BST = Delete(BST, X);
}
printf("Inorder:"); InorderTraversal(BST); printf("\n");
return 0;
}
void PreorderTraversal( BinTree BT ){
if(BT == NULL) return;
printf(" %d",BT->Data);
PreorderTraversal(BT->Left);
PreorderTraversal(BT->Right);
}
void InorderTraversal( BinTree BT ){
if(BT == NULL) return;
InorderTraversal(BT->Left);
printf(" %d",BT->Data);
InorderTraversal(BT->Right);
}
BinTree Insert( BinTree BST, ElementType X ){
if(BST == NULL){
BinTree t = (BinTree) malloc(sizeof (BinTree));
t->Data = X;
t->Left = t->Right = NULL;
BST = t;
}
else
(X<BST->Data?(BST->Left = Insert(BST->Left,X)):(BST->Right=Insert(BST->Right,X)));
return BST;
}
BinTree Delete( BinTree BST, ElementType X ){
if(BST == NULL)
puts("Not Found");
else {
if (X == BST->Data) {
if (BST->Left != NULL && BST->Right != NULL) {
BinTree t = FindMax(BST->Left);
BST->Data = t->Data;
BST->Left = Delete(BST->Left, t->Data);
} else {
BST =(BST->Left ? BST->Left : BST->Right);
}
} else {
X > BST->Data ? (BST->Right = (Delete(BST->Right, X))) : (BST->Left = Delete(BST->Left, X));
}
}
return BST;
}
Position Find( BinTree BST, ElementType X ){
if(BST == NULL){
return NULL;
}
if(BST->Data == X){
return BST;
}
return X < BST->Data ? Find(BST->Left,X): Find(BST->Right,X);
}
Position FindMin( BinTree BST ){
if(BST != NULL) {
return BST->Left ? FindMin(BST->Left) : BST;
}
}
Position FindMax( BinTree BST ){
if(BST != NULL){
return BST->Right? FindMax(BST->Right):BST;
}
}
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